Solve (8x^7/y^-7)^3

$$( \frac { 8 x ^ { 7 } } { y ^ { - 7 } } ) ^ { 3 }$$

Evaluate

$$512\left(xy\right)^{21}$$

Solution Steps

To raise \frac{8x^{7}}{y^{-7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(8x^{7}\right)^{3}}{\left(y^{-7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -7 and 3 to get -21.

$$\frac{\left(8x^{7}\right)^{3}}{y^{-21}}$$

Expand \left(8x^{7}\right)^{3}.

$$\frac{8^{3}\left(x^{7}\right)^{3}}{y^{-21}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{8^{3}x^{21}}{y^{-21}}$$

Calculate 8 to the power of 3 and get 512.

$$\frac{512x^{21}}{y^{-21}}$$

Expand

$$512\left(xy\right)^{21}$$

Solution Steps

To raise \frac{8x^{7}}{y^{-7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(8x^{7}\right)^{3}}{\left(y^{-7}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -7 and 3 to get -21.

$$\frac{\left(8x^{7}\right)^{3}}{y^{-21}}$$

Expand \left(8x^{7}\right)^{3}.

$$\frac{8^{3}\left(x^{7}\right)^{3}}{y^{-21}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\frac{8^{3}x^{21}}{y^{-21}}$$

Calculate 8 to the power of 3 and get 512.

$$\frac{512x^{21}}{y^{-21}}$$